1991 AIME Problems/Problem 2
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Problem
Rectangle 
has sides 
of length 4 and 
of length 3. Divide into 168 congruent segments with points 
, and divide into 168 congruent segments with points 
. For 
, draw the segments 
. Repeat this construction on the sides 
and 
, and then draw the diagonal 
. Find the sum of the lengths of the 335 parallel segments drawn.
Solution
The length of the diagonal is 
(a 3-4-5 right triangle). For each 
, is the hypotenuse of a 
right triangle with sides of 
. Thus, its length is 
.
The sum we are looking for is 
. Using the formula for the sum of the first natural numbers, we find that the solution is 
.
See also
| 1991 AIME (Problems • Resources) | ||
| Preceded by Problem 1 | Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
